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# Finding roots - C1 Watch

1. First of all, I completely agree with bb193's statement - you need to be equally proficient with solving quadratics by factorising, CTS and the quadratic equation.

(Original post by Conal09)
Can you just confirm this for me? So you have -2 1/2 and then, to get -5, you multiply through by 2? And in doing so you get 2(x-1)^2? That's where I went wrong in that method
Sorry, couldn't reply earlier because I lost track of time and have to run (ice-skate?) to the bus stop to get into town!

Sorry if this explanation becomes patronising at any point, it isn't meant to be.

When you expand the brackets (a+b)^2, you get a^2 + 2ab + b^2.

What I've done is rewrite (x^2 - 2x) into a set of squared brackets. Hence the (x-1)^2. These two forms aren't actually equal - if you multiply out (x-1)^2 you'll have an extra +1 because of the (-1)*(-1) term. To make (x^2 - 2x) into (x-1)^2, we need to subtract 1 as well.

Hence, the (-1 - (3/2)). This multiplied by 2 gives (-2 - 3) = -5.

EDIT: I think that was possibly the least clear explanation I've ever given. PM if it still doesn't make sense.
2. (Original post by Conal09)
Can you just confirm this for me? So you have -2 1/2 and then, to get -5, you multiply through by 2? And in doing so you get 2(x-1)^2? That's where I went wrong in that method
Pretty much.

What we want to do is multiply out the brackets so we can simplify it all. The 2 on the outside makes it really annoying to solve for x, because x is inside. To get rid of the 2 we can multiply everything inside the square brackets by 2. Do each bit one by one:

(x-1)² multiplied by 2 is 2(x-1)².
-1 multiplied by 2 is -2
-3/2 multiplied by 2 is -3

So what we have is:

2(x-1)²-2-3=0 which is the same as writing 2(x-1)²-5=0

You can then solve for x.

-------

Another way of doing it is straight away dividing both sides of by 2, because all we want to do is get rid of the big 2 on the outside and this would do the trick nice and quickly.

If we pretend you can see that the original equation could be written as .

Dividing 2z by 2 would give you z, and dividing 0 by 2 would give you 0.
So what you're left with is:

;

Remember that 1 could be rewritten as ;

Grouping all the numbers together on one side, and the x on the other side, you end up with:

3. Btw: is the same as root 5 over root 2. You get root 10 over 2 by multiplying top and bottom by root 2.

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Updated: December 21, 2010
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